A204658 Numbers n such that n!10-1 is prime.

3, 4, 6, 8, 12, 20, 40, 48, 60, 62, 70, 84, 88, 168, 240, 258, 372, 760, 932, 1010, 2110, 2464, 2490, 2702, 3180, 4744, 6024, 8858, 9060, 10322, 13382, 15778, 19322, 22372, 22928, 25344, 28050, 40604, 42282, 45884, 52428, 58250, 81220, 93612, 108650

Offset: 1

Author

M. F. Hasler, Jan 17 2012

Keywords

• nonn
• hard

Comments

n!10 = product( n-10k, 0 <= k < n/10 ).

See also links in A156165.

a(1)-a(40) are proved prime by deterministic tests of pfgw. - Robert Price, Jun 11 2012

a(41) > 50000. - Robert Price, Jun 11 2012

Links

• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!10-1.

Crossrefs

Cf. A204657, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], PrimeQ[MultiFactorial[#, 10] - 1] & ] (* Robert Price, Apr 19 2019 *)

PARI

for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)-1)& print1(n","))

Extensions

a(26)-a(40) from Robert Price, Jun 11 2012

a(41)-a(45) from Ken Davis link entered by Robert Price, Apr 19 2019